Explain the relationships among financial decisions, return, risk, and

LG 6 Explain the relationships among financial decisions, return, risk, and

the firm’s value. In a stable economy, any action of the financial manager that increases the level of expected dividends without changing risk should increase share value; any action that reduces the level of expected dividends without changing risk should reduce share value. Similarly, any action that increases risk (required return) will reduce share value; any action that reduces risk will increase share value. An assessment of the combined effect of return and risk on stock value must be part of the financial decision-making process.

Opener-in-Review

A123 shares were originally offered for sale at a price of $13.50. Three months later, the stock traded for about $18. What return did investors earn over this period? On November 10, 2009, A123 reported its 3rd quarter financial results. From November 9 to November 11, the firm’s stock price fell from $17.85 to $16.88. Given that A123 has 102 million shares outstanding, what were the dollar and percentage losses that shareholders endured in the days surrounding the earnings release? Over the same three days (November 9–11), the Nasdaq stock index moved up 0.6%. How does this influence your thinking about A123’s stock performance around this time?

Self-Test Problems (Solutions in Appendix)

LG 4 ST7–1 Common stock valuation Perry Motors’ common stock just paid its annual dividend of $1.80 per share. The required return on the common stock is 12%. Estimate the value of the common stock under each of the following assumptions about the dividend:

a. Dividends are expected to grow at an annual rate of 0% to infinity. b. Dividends are expected to grow at a constant annual rate of 5% to infinity. c. Dividends are expected to grow at an annual rate of 5% for each of the next

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Stock Valuation

LG 5 ST7–2 Free cash flow valuation Erwin Footwear wishes to assess the value of its Active Shoe Division. This division has debt with a market value of $12,500,000 and no

preferred stock. Its weighted average cost of capital is 10%. The Active Shoe Division’s estimated free cash flow each year from 2013 through 2016 is given in the following table. Beyond 2016 to infinity, the firm expects its free cash flow to grow at 4% annually.

Year (t)

Free cash flow (FCF t )

a. Use the free cash flow valuation model to estimate the value of Erwin’s entire

Active Shoe Division. b. Use your finding in part a along with the data provided above to find this divi-

sion’s common stock value. c. If the Active Shoe Division as a public company will have 500,000 shares

outstanding, use your finding in part b to calculate its value per share.

Warm-Up Exercises All problems are available in

LG 1 E7–1 A balance sheet balances assets with their sources of debt and equity financing. If a corporation has assets equal to $5.2 million and a debt ratio of 75.0%, how much debt does the corporation have on its books?

LG 2 E7–2 Angina, Inc., has 5 million shares outstanding. The firm is considering issuing an additional 1 million shares. After selling these shares at their $20 per share offering

price and netting 95% of the sale proceeds, the firm is obligated by an earlier agree- ment to sell an additional 250,000 shares at 90% of the offering price. In total, how much cash will the firm net from these stock sales?

LG 2 E7–3 Figurate Industries has 750,000 shares of cumulative preferred stock outstanding. It has passed the last three quarterly dividends of $2.50 per share and now (at the end of the current quarter) wishes to distribute a total of $12 million to its shareholders. If Figurate has 3 million shares of common stock outstanding, how large a per-share common stock dividend will it be able to pay?

LG 3 E7–4 Today the common stock of Gresham Technology closed at $24.60 per share, down $0.35 from yesterday. If the company has 4.6 million shares outstanding and annual earnings of $11.2 million, what is its P/E ratio today? What was its P/E ratio yes- terday?

LG 4 E7–5 Stacker Weight Loss currently pays an annual year-end dividend of $1.20 per share. It plans to increase this dividend by 5% next year and maintain it at the new level for the foreseeable future. If the required return on this firm’s stock is 8%, what is

PART 3

Valuation of Securities

LG 6 E7–6 Brash Corporation initiated a new corporate strategy that fixes its annual dividend at $2.25 per share forever. If the risk-free rate is 4.5% and the risk premium on

Brash’s stock is 10.8%, what is the value of Brash’s stock?

Problems All problems are available in

LG 2 P7–1 Authorized and available shares Aspin Corporation’s charter authorizes issuance of 2,000,000 shares of common stock. Currently, 1,400,000 shares are outstanding, and 100,000 shares are being held as treasury stock. The firm wishes to raise $48,000,000 for a plant expansion. Discussions with its investment bankers indicate that the sale of new common stock will net the firm $60 per share.

a. What is the maximum number of new shares of common stock that the firm can sell without receiving further authorization from shareholders?

b. Judging on the basis of the data given and your finding in part a, will the firm be able to raise the needed funds without receiving further authorization?

c. What must the firm do to obtain authorization to issue more than the number of

shares found in part a? LG 2 P7–2 Preferred dividends Slater Lamp Manufacturing has an outstanding issue of pre-

ferred stock with an $80 par value and an 11% annual dividend. a. What is the annual dollar dividend? If it is paid quarterly, how much will be paid

each quarter? b. If the preferred stock is noncumulative and the board of directors has passed the

preferred dividend for the last 3 quarters, how much must be paid to preferred stockholders in the current quarter before dividends are paid to common stock- holders?

c. If the preferred stock is cumulative and the board of directors has passed the pre- ferred dividend for the last 3 quarters, how much must be paid to preferred stockholders in the current quarter before dividends are paid to common stock- holders?

LG 2 P7–3 Preferred dividends In each case in the following table, how many dollars of pre- ferred dividends per share must be paid to preferred stockholders in the current

period before common stock dividends are paid?

Dividend per

Periods of

Case

Type

Par value

share per period

dividends passed

A Cumulative

B Noncumulative

C Noncumulative

D Cumulative

E Cumulative

LG 2 P7–4 Convertible preferred stock Valerian Corp. convertible preferred stock has a fixed

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Stock Valuation

stock pays a dividend of $10.00 per share per year. The common stock currently sells for $20.00 per share and pays a dividend of $1.00 per share per year.

a. Judging on the basis of the conversion ratio and the price of the common shares, what is the current conversion value of each preferred share?

b. If the preferred shares are selling at $96.00 each, should an investor convert the preferred shares to common shares?

c. What factors might cause an investor not to convert from preferred to common stock?

Personal Finance Problem LG 4 P7–5 Common stock valuation—Zero growth Scotto Manufacturing is a mature firm in the machine tool component industry. The firm’s most recent common stock divi- dend was $2.40 per share. Because of its maturity as well as its stable sales and earn- ings, the firm’s management feels that dividends will remain at the current level for the foreseeable future.

a. If the required return is 12%, what will be the value of Scotto’s common stock? b. If the firm’s risk as perceived by market participants suddenly increases, causing

the required return to rise to 20%, what will be the common stock value? c. Judging on the basis of your findings in parts a and b, what impact does risk

have on value? Explain. Personal Finance Problem

LG 4 P7–6 Common stock value—Zero growth Kelsey Drums, Inc., is a well-established sup- plier of fine percussion instruments to orchestras all over the United States. The

company’s class A common stock has paid a dividend of $5.00 per share per year for the last 15 years. Management expects to continue to pay at that amount for the foreseeable future. Sally Talbot purchased 100 shares of Kelsey class A common

10 years ago at a time when the required rate of return for the stock was 16%. She wants to sell her shares today. The current required rate of return for the stock is 12%. How much capital gain or loss will Sally have on her shares?

LG 4 P7–7 Preferred stock valuation Jones Design wishes to estimate the value of its out-

standing preferred stock. The preferred issue has an $80 par value and pays an annual dividend of $6.40 per share. Similar-risk preferred stocks are currently earning a 9.3% annual rate of return.

a. What is the market value of the outstanding preferred stock? b. If an investor purchases the preferred stock at the value calculated in part a, how

much does she gain or lose per share if she sells the stock when the required return on similar-risk preferred stocks has risen to 10.5%? Explain.

LG 4 P7–8 Common stock value—Constant growth Use the constant-growth model (Gordon

growth model) to find the value of each firm shown in the following table.

Firm Dividend expected next year Dividend growth rate Required return

A $1.20

13% B 4.00 5 15 C 0.65 10 14

D 6.00 8 9 E 2.25 8 20

PART 3

Valuation of Securities

LG 4 P7–9 Common stock value—Constant growth McCracken Roofing, Inc., common stock paid a dividend of $1.20 per share last year. The company expects earnings and divi-

dends to grow at a rate of 5% per year for the foreseeable future. a. What required rate of return for this stock would result in a price per share

of $28? b. If McCracken expects both earnings and dividends to grow at an annual rate of

10%, what required rate of return would result in a price per share of $28?

Personal Finance Problem

LG 4 P7–10 Common stock value—Constant growth Elk County Telephone has paid the divi-

dends shown in the following table over the past 6 years.

Year

Dividend per share

The firm’s dividend per share next year is expected to be $3.02. a. If you can earn 13% on similar-risk investments, what is the most you would be

willing to pay per share? b. If you can earn only 10% on similar-risk investments, what is the most you

would be willing to pay per share? c. Compare and contrast your findings in parts a and b, and discuss the impact of

changing risk on share value.

LG 4 P7–11 Common stock value—Variable growth Newman Manufacturing is considering a cash purchase of the stock of Grips Tool. During the year just completed, Grips earned $4.25 per share and paid cash dividends of $2.55 per share ( D 0 = $2.55) . Grips’ earnings and dividends are expected to grow at 25% per year for the next 3 years, after which they are expected to grow at 10% per year to infinity. What is the maximum price per share that Newman should pay for Grips if it has a required return of 15% on investments with risk characteristics similar to those of Grips?

Personal Finance Problem

LG 4 P7–12 Common stock value—Variable growth Home Place Hotels, Inc., is entering into a 3-year remodeling and expansion project. The construction will have a limiting

effect on earnings during that time, but when it is complete, it should allow the com- pany to enjoy much improved growth in earnings and dividends. Last year, the com- pany paid a dividend of $3.40. It expects zero growth in the next year. In years 2 and 3, 5% growth is expected, and in year 4, 15% growth. In year 5 and thereafter, growth should be a constant 10% per year. What is the maximum price per share that an investor who requires a return of 14% should pay for Home Place Hotels

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Stock Valuation

LG 4 P7–13 Common stock value—Variable growth Lawrence Industries’ most recent annual dividend was $1.80 per share ( D 0 = $1.80) , and the firm’s required return is 11%.

Find the market value of Lawrence’s shares when: a. Dividends are expected to grow at 8% annually for 3 years, followed by a 5% constant annual growth rate in years 4 to infinity.

b. Dividends are expected to grow at 8% annually for 3 years, followed by a 0% constant annual growth rate in years 4 to infinity.

c. Dividends are expected to grow at 8% annually for 3 years, followed by a 10% constant annual growth rate in years 4 to infinity.

Personal Finance Problem LG 4 P7–14 Common stock value—All growth models You are evaluating the potential pur-

chase of a small business currently generating $42,500 of after-tax cash flow

( D 0 = $42,500) . On the basis of a review of similar-risk investment opportunities, you must earn an 18% rate of return on the proposed purchase. Because you are relatively uncertain about future cash flows, you decide to estimate the firm’s value using several possible assumptions about the growth rate of cash flows.

a. What is the firm’s value if cash flows are expected to grow at an annual rate of 0% from now to infinity?

b. What is the firm’s value if cash flows are expected to grow at a constant annual rate of 7% from now to infinity?

c. What is the firm’s value if cash flows are expected to grow at an annual rate of 12% for the first 2 years, followed by a constant annual rate of 7% from year 3 to infinity?

LG 5 P7–15 Free cash flow valuation Nabor Industries is considering going public but is unsure of a fair offering price for the company. Before hiring an investment banker to assist

in making the public offering, managers at Nabor have decided to make their own estimate of the firm’s common stock value. The firm’s CFO has gathered data for performing the valuation using the free cash flow valuation model.

The firm’s weighted average cost of capital is 11%, and it has $1,500,000 of debt at market value and $400,000 of preferred stock at its assumed market value. The estimated free cash flows over the next 5 years, 2013 through 2017, are given below. Beyond 2017 to infinity, the firm expects its free cash flow to grow by 3% annually.

Year (t)

Free cash flow (FCF t )

a. Estimate the value of Nabor Industries’ entire company by using the free cash flow valuation model.

b. Use your finding in part a, along with the data provided above, to find Nabor Industries’ common stock value.

c. If the firm plans to issue 200,000 shares of common stock, what is its estimated

PART 3

Valuation of Securities

Personal Finance Problem

LG 5 P7–16 Using the free cash flow valuation model to price an IPO Assume that you have an opportunity to buy the stock of CoolTech, Inc., an IPO being offered for $12.50 per share. Although you are very much interested in owning the company, you are con- cerned about whether it is fairly priced. To determine the value of the shares, you have decided to apply the free cash flow valuation model to the firm’s financial data that you’ve developed from a variety of data sources. The key values you have com- piled are summarized in the following table.

Free cash flow Year (t)

FCF t

Other data

Growth rate of FCF, beyond 2013 to infinity = 2%

Weighted average cost of capital = 8%

Market value of all debt = $2,700,000

Market value of preferred stock = $1,000,000 Number of shares of common stock outstanding = 1,100,000

a. Use the free cash flow valuation model to estimate CoolTech’s common stock value per share.

b. Judging on the basis of your finding in part a and the stock’s offering price,

should you buy the stock? c. On further analysis, you find that the growth rate in FCF beyond 2016 will be

3% rather than 2%. What effect would this finding have on your responses in parts a and b?

LG 5 P7–17 Book and liquidation value The balance sheet for Gallinas Industries is as follows.

Gallinas Industries Balance Sheet December 31

Assets Liabilities and Stockholders’ Equity

$100,000 Marketable securities

Cash

Accounts payable

30,000 Accounts receivable

Notes payable

30,000 Inventories

Accrued wages

$160,000 Total current assets

Total current liabilities

$180,000 Land and buildings (net)

Long-term debt

$ 80,000 Machinery and equipment

Preferred stock

260,000 Total fixed assets (net)

Common stock (10,000 shares)

100,000 Total assets

Retained earnings

Total liabilities and stockholders’ equity $780,000

Additional information with respect to the firm is available: (1) Preferred stock can be liquidated at book value. (2) Accounts receivable and inventories can be liquidated at 90% of book value. (3) The firm has 10,000 shares of common stock outstanding.

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Stock Valuation

(5) Land and buildings can be liquidated at 130% of book value. (6) Machinery and equipment can be liquidated at 70% of book value. (7) Cash and marketable securities can be liquidated at book value.

Given this information, answer the following: a. What is Gallinas Industries’ book value per share? b. What is its liquidation value per share?

c. Compare, contrast, and discuss the values found in parts a and b.

LG 5 P7–18 Valuation with price/earnings multiples For each of the firms shown in the fol- lowing table, use the data given to estimate its common stock value employing

price/earnings (P/E) multiples.

Firm

Expected EPS

Price/earnings multiple

A $3.00

6.2 B 4.50 10.0 C 1.80 12.6

D 2.40 8.9 E 5.10 15.0

LG 6 P7–19 Management action and stock value REH Corporation’s most recent dividend was $3 per share, its expected annual rate of dividend growth is 5%, and the required return is now 15%. A variety of proposals are being considered by management to redirect the firm’s activities. Determine the impact on share price for each of the fol- lowing proposed actions, and indicate the best alternative.

a. Do nothing, which will leave the key financial variables unchanged. b. Invest in a new machine that will increase the dividend growth rate to 6% and

lower the required return to 14%. c. Eliminate an unprofitable product line, which will increase the dividend growth

rate to 7% and raise the required return to 17%. d. Merge with another firm, which will reduce the growth rate to 4% and raise the

required return to 16%. e. Acquire a subsidiary operation from another manufacturer. The acquisition

should increase the dividend growth rate to 8% and increase the required return to 17%.

LG 4 LG 6 P7–20 Integrative—Risk and Valuation Given the following information for the stock of Foster Company, calculate the risk premium on its common stock.

Current price per share of common $50.00 Expected dividend per share next year

$ 3.00 Constant annual dividend growth rate

9% Risk-free rate of return

7% LG 4 LG 6 P7–21 Integrative—Risk and valuation Giant Enterprises’ stock has a required return of

14.8%. The company, which plans to pay a dividend of $2.60 per share in the

PART 3

Valuation of Securities

consistent with that experienced over the 2006–2012 period, when the following dividends were paid:

Year

Dividend per share

a. If the risk-free rate is 10%, what is the risk premium on Giant’s stock? b. Using the constant-growth model, estimate the value of Giant’s stock.

c. Explain what effect, if any, a decrease in the risk premium would have on the

value of Giant’s stock.

LG 4 LG 6 P7–22 Integrative—Risk and Valuation Hamlin Steel Company wishes to determine the value of Craft Foundry, a firm that it is considering acquiring for cash. Hamlin wishes to determine the applicable discount rate to use as an input to the constant- growth valuation model. Craft’s stock is not publicly traded. After studying the required returns of firms similar to Craft that are publicly traded, Hamlin believes that an appropriate risk premium on Craft stock is about 5%. The risk-free rate is currently 9%. Craft’s dividend per share for each of the past 6 years is shown in the following table.

Year

Dividend per share

a. Given that Craft is expected to pay a dividend of $3.68 next year, determine the maximum cash price that Hamlin should pay for each share of Craft.

b. Describe the effect on the resulting value of Craft of: (1) A decrease in its dividend growth rate of 2% from that exhibited over the

2007–2012 period. (2) A decrease in its risk premium to 4%.

LG 4 P7–23 ETHICS PROBLEM Melissa is trying to value Generic Utility, Inc.’s, stock, which is clearly not growing at all. Generic declared and paid a $5 dividend last year. The required rate of return for utility stocks is 11%, but Melissa is unsure about the

CHAPTER 7

Stock Valuation

1% “credibility” risk premium to the required return as part of her valuation analysis.

a. What is the value of Generic’s stock, assuming that the financials are trust-

worthy? b. What is the value of Generic’s stock, assuming that Melissa includes the extra

1% “credibility” risk premium? c. What is the difference between the values found in parts a and b, and how might

one interpret that difference?

Spreadsheet Exercise

You are interested in purchasing the common stock of Azure Corporation. The firm recently paid a dividend of $3 per share. It expects its earnings—and hence its divi- dends—to grow at a rate of 7% for the foreseeable future. Currently, similar-risk stocks have required returns of 10%.